If you hit more in the center of the blade face, the contact feels better. If you are off a little and hit more towards one of the edges of the blade, the shot will not feel quite as good. This is particularly the case on harder shots.
Part of why it this happens is that, when you hit nearer to the edges of the blade, you get more of the kind of vibration you would not want to feel on a TT shot. With carbon blades, carbon masks vibrations so, often, people say carbon blades have a larger sweet spot. From the standpoint of developing technique, I am not so sure you would want that. This is equivalent to saying, you can mess up and use worse technique and poor contact and get away with it.
So, for a developing player, a blade that will mask mistakes in contact and technique will make it take longer for the player to improve the quality of their contact. For a high level player, they already have good enough technique for this not to effect their future development.
I think, originally, the idea came from tennis rackets. With a racket with strings, it is clear that, in the center, the strings will give the most rebound. Off center, you will get less rebound and more unwanted vibrations. It is not as noticeable in a TT racket. But it is still similar. And you can feel it. Closer to the center, the contact will feel more solid. Closer to the edges, contact will feel weaker and create unwanted vibrations. Wood vibrates less than the strings and material of the frame of a tennis racket. But wood still vibrates. And hitting off center, the wood will flex and vibrate significantly more.
That is at least when Sweet Spot refers to in racket sports. Where the ball contact feels the best.